The Source Of Lobatchevsky’ S Geometry

In this paper, by reading Lobatchevsky’s geometry books, using literature research and his-torical analysis method, comparative research method and citation analysis method of the previ-ous research results, the author explored systematically the creation process of Lobatchevsky’s geometry and its spread.The main work was as following:Firstly,based on the mathematicians’ exploring towards the Euclidean fifth postulate, and concerning from the test certification to fifth postulate, the budding thought of non-Euclidean geometry and the equivalent propositions of fifth postulate these three aspects respectively the mathematicians’contribution of non-Euclidean geometry before18th Century was discussed in this paper,pointing out the achievements,defects and deficiencies of the forerunners to non-Euclidean geometry which indicates that the non-Euclidean geometry is limited to by the time.Secondly,by the in-depth studying towards non-Euclidean geometry research work of Gauss, Bolyai and Lobachevsky and their transformation process of geometric thought, the author tried to point out:the reason why Gauss did not publish the works on non-Euclidean geometry works is that non-Euclidean geometry is still far from the degree of maturity as he expected, rather than he do not have the courage to publish.What’s more,the paper revealed the environment in which Lobachevsky get his geometry results. On this basis, comparing these three founders’ work, the author summarized and pointed out the similarities and differences. The same point:1, they all draw the parallel angle formula;2, they all established the independent formula of spherical triangle in the parallel postulate;3, they all admitted that the non-Euclidean geometry can be applied to real space. The different points:1, Gauss and Bolya did not have the proof to the compatibility of new geometric proof, but Lobachevsky had done;2, Lobachevsky’s main job was to find out the uniqueness of non-Euclidean geometry, however, Bolya mainly looked for the similarities between Euclidean geometry and non-Euclidean geometry.Thirdly,Through reading Lobachevsky’s original literature " on the geometry principle ", the geometry thought from Lobachevsky’s non-Euclidean was drawn. And from the Lobachevsky function, triangle theory, theory of area and compatibility and realistic space these aspects,the paper introduced the basic content of the Lobachevsky’s geometry. According to Lobachevsky’s original theory " parallel lines ", the Lobachevsky function was derived firstly, and on the basis of it, the triangle theory of Lobachevsky was described,and also put forwards that Lobachevsky functions provides a basic condition for the new geometric theory, while Lobachevsky triangle formula outlined the system outline of the new geometry. Finally, the compatibility and the real space of the new geometry were described.Fourthly,in this part,the author mainly described specifically the development of non-Euclidean geometry and its confirmation and influence,and the difficult process of acceptance to non-Euclidean geometry. In addition, the paper pointed out an important impact of the es-tablishment of non-Euclidean geometry that it was to force people to establish a new geometric concept, and changed people’s understanding to Mathematics fundamentally.